Robust Adaptive Spacecraft Array Derivative Analysis - Vogt, J.; Blagau, A.; Pick, L. (Earth and space science (Hoboken, N.J.), 2020)
Multispacecraft missions such as Cluster, Themis, Swarm, and MMS contribute to the exploration of geospace with their capability to produce gradient and curl estimates from sets of spatially distributed in situ measurements. This paper combines all existing estimators of the reciprocal vector family for spatial derivatives and their errors. The resulting framework proves to be robust and adaptive in the sense that it works reliably for arrays with arbitrary numbers of spacecraft and possibly degenerate geometries. The analysis procedure is illustrated using synthetic data as well as magnetic measurements from the Cluster and Swarm missions. An implementation of the core algorithm in Python is shown to be compact and computationally efficient so that it can be easily integrated in the various free and open source packages for the Space Physics and Heliophysics community. Plain Language Summary The space environment of the Earth is studied using spacecraft measurements of physical variables. To resolve their variability in both space in time, constellations of several spacecraft such as Cluster, Themis, Swarm, and MMS are needed. This report combines methods to determine the spatial variability from distributed spacecraft observations in a unifying software framework. The approach works for arbitrary numbers of spacecraft in the constellation and adapts to possibly degenerate geometries that otherwise could lead to large errors. The analysis method is validated using synthetic data and then applied to magnetic measurements from the Cluster and Swarm missions. Implementation in the popular numerical software Python is shown to be compact and computationally efficient and presented in a way that facilitates easy integration in existing free and open source software. Key Points A unifying and robust framework for satellite array gradient and curl estimations is introduced The adaptive algorithm handles arbitrary numbers of satellites and degenerate arrays A numerically efficient implementation of the algorithm in Python is presented